Weak dual residuations applied to tropical linear equations

An extension to an algorithm of R.A. Cuninghame-Green and K. Zimmermann for solving equations with residuated functions is presented. This extension relies on the concept of weak residuation and in the so-called “strong property”. It is shown that a contextualization of this method to tropical linear equations, which will be denoted as Primal Method (in contrast with the Dual Method, another algorithm described in literature), generates a non-decreasing sequence which converges to the smallest solution in a special semimodule. It is also shown the connections of this method with previously published works

On Max-Plus Linear Dynamical System Theory: The Regulation Problem

A class of timed discrete event systems can be modeled by using Timed-Event Graphs, a class of timed Petri nets that can have its firing dynamic described by using an algebra called “Max-plus algebra”. For this kind of systems it may be desirable to enforce some timing constraints in steady state. In this paper, this problem is called a “max-plus regulation problem”. In this context we show a necessary condition for solving these regulation problems and in addition that this condition is sufficient for a large class of problems. The obtained controller is a simple linear static state feedback and can be computed using efficient pseudo-polynomial algorithms. Simulation results will illustrate the applicability of the proposed methodology

On max-plus linear dynamical system theory: the observation problem

In this paper, we are interested in the general problem of estimating a linear function of the states for a given Max-Plus linear dynamical system. More precisely, using only the current and past inputs/outputs of the system, we want to construct a sequence that converges in a finite number of steps to the value given by a linear function of the states, for all initial conditions of the system. We provide necessary and sufficient conditions to solve this general problem. We also define and study a Max-Plus version of the well-known Luenberger observer, which is a subclass of the general problem that we are interested in, and we also provide necessary and sufficient conditions to solve this particular problem of observer synthesis. Finally, we show that there are important connections between results in the Max-Plus domain and associated results in the standard linear systems theory

Study of the reaction of grafting acrylamide onto xanthan gum

AbstractThe present study aimed to study the reaction conditions of grafting of acrylamide on xanthan gum. It was analyzed the influence of reaction conditions, mainly type of initiator activation, initiator concentration and initiator/acrylamide ratio, on graft parameters and copolymer properties. Potassium persulfate was employed as an initiator and heating or N,N,N′,N′-tetramethylethylenediamine was used to activate the initiator. Reaction time and initiator concentration were varied and final values for grafting percentage and grafting efficiency were the same for both methods, whereas speed in reaching these values differs from one technique to another. We found that reaction time was inversely proportional to intrinsic viscosity, likely due to main chain degradation promoted by potassium persulfate (KPS); furthermore, the increasing in the KPS concentration lowers grafting percentage, acrylamide conversion and chain degradation, possibly as a result of O2 formation at high KPS concentrations

Influence Of Backing And Matching Layers In Ultrasound Transducers Performance

In this work we have investigated the influence of the backing layer composition and the matching layer thickness in the performance of ultrasound transducers constructed with piezoelectric ceramic discs. We have constructed transducers with backing layers of different compositions, using mixtures of epoxy with alumina powder and/or Tungsten powder and with λ/4 or 3λ/4 thickness epoxy matching layers. The evaluation tests were performed in pulse-echo mode, with a flat target, and in transmission/reception mode, with a calibrated PVDF hydrophone. The acoustical field emitted by each transducer was mapped in order to measure the on-axis and transverse field profiles, the aperture size and the beam spreading. The bandwidths of the transducers were determined in pulse-echo mode. Comparing the evaluation tests results of two transducers constructed with the same backing layer, the one constructed with λ/4 thickness epoxy matching layer showed better performance. The results showed that the transducers constructed with epoxy, alumina and Tungsten powders backing layers have larger bandwidth. The larger depth of field was measured for transducers constructed with epoxy and Tungsten powder backing layers. These transducers and those constructed with epoxy, Tungsten and alumina powders backing layers showed the larger field intensities in the measured transverse profiles.50358696(1999) Standard Guide for Evaluating Characteristics of Ultrasonic Search Units, , ASTM E-1065 1999Desilets, C.S., Fraser, J.D., Kino, G.S., The design of efficient broad-band piezoelectric transducers (1978) IEEE Transactions on Sonics and Ultrasonics, SU-25 (3), pp. 115-125(1996) Ultrasonics Real Time Pulse-echo Systems: Test Procedures to Determine Performance Specification, , IEC-1390(1989) IEEE Guide for Medical Ultrasound Field Parameter Measurements, , IEEE American National Standard Std 790(1978) IEEE Standard on Piezoelectricity, , IEEE American National Standard Std 176Inoue, T., Ohta, M., Takahashi, S., Design of ultrasonic transducers with multiple acoustic matching layers for medical applications (1987) IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 34 (1)Lockwood, G.R., Turnbull, D.H., Foster, F.S., Fabrication of high frequency spherically shaped ceramic transducers (1994) IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 41 (2)Mitra, R., Saksena, T.K., Study on the vibrational characteristics of ultrasonic transducers using tapered piezoelectric ceramic elements (1995) Journal of the Acoustical Society of America, 58 (2)Sayers, C.M., Tait, C.E., Ultrasonic properties of transducer backing (1984) Ultrasonics, 22 (2

On the Steady State Control of Timed Event Graphs with Firing Date Constraints

Two algorithms for solving a specific class of steadystate control problems for Timed Event Graphs are presented. In the first, asymptotic convergence to the desired set is guaranteed. The second algorithm, which builds on from the recent developments in the spectral theory of min-max functions, guarantees Lyapunov stability since the distance between the actual state and the desired set never increases. Simulation results show the efficiency of the proposed approach in a problem of moderate complexity

An Observer for Tropical Linear Event-Invariant Dynamical Systems

This paper presents a sufficient condition to solve the observation problem in tropical linear event-invariant dynamical systems, where a linear functional of the states can be observed in a finite number of steps using only the information from inputs and outputs. Using the residuation theory, this solvability condition can be easily implemented in polynomial time. Moreover, the main results are applied to state feedback control using only the observed states based on the measurements of the original states in the system. Furthermore, the main results are implemented in the perturbation observation problem for tropical linear event-invariant dynamical systems, where the system matrices are perturbed in intervals.